A revised edition that explores random numbers, probability, and statistical inference at an introductory mathematical level Written in an engaging and entertaining manner, the revised and updated second edition of Probably Not continues to offer an informative guide to probability and prediction. The expanded second edition contains problem and solution sets. In addition, the book’s illustrative examples reveal how we are living in a statistical world, what we can expect, what we really know based upon the information at hand and explains when we only think we know something. The author introduces the principles of probability and explains probability distribution functions. The book covers combined and conditional probabilities and contains a new section on Bayes Theorem and Bayesian Statistics, which features some simple examples including the Presecutor’s Paradox, and Bayesian vs. Frequentist thinking about statistics. New to this edition is a chapter on Benford’s Law that explores measuring the compliance and financial fraud detection using Benford’s Law. This book: Contains relevant mathematics and examples that demonstrate how to use the concepts presented Features a new chapter on Benford’s Law that explains why we find Benford’s law upheld in so many, but not all, natural situations Presents updated Life insurance tables Contains updates on the Gantt Chart example that further develops the discussion of random events Offers a companion site featuring solutions to the problem sets within the book Written for mathematics and statistics students and professionals, the updated edition of Probably Not: Future Prediction Using Probability and Statistical Inference, Second Edition combines the mathematics of probability with real-world examples. LAWRENCE N. DWORSKY, PhD, is a retired Vice President of the Technical Staff and Director of Motorola’s Components Research Laboratory in Schaumburg, Illinois, USA. He is the author of Introduction to Numerical Electrostatics Using MATLAB from Wiley.

Probability is the bedrock of machine learning. You cannot develop a deep understanding and application of machine learning without it. Cut through the equations, Greek letters, and confusion, and discover the topics in probability that you need to know. Using clear explanations, standard Python libraries, and step-by-step tutorial lessons, you will discover the importance of probability to machine learning, Bayesian probability, entropy, density estimation, maximum likelihood, and much more.

A revised edition that explores random numbers, probability, and statistical inference at an introductory mathematical level Written in an engaging and entertaining manner, the revised and updated second edition of Probably Not continues to offer an informative guide to probability and prediction. The expanded second edition contains problem and solution sets. In addition, the book’s illustrative examples reveal how we are living in a statistical world, what we can expect, what we really know based upon the information at hand and explains when we only think we know something. The author introduces the principles of probability and explains probability distribution functions. The book covers combined and conditional probabilities and contains a new section on Bayes Theorem and Bayesian Statistics, which features some simple examples including the Presecutor’s Paradox, and Bayesian vs. Frequentist thinking about statistics. New to this edition is a chapter on Benford’s Law that explores measuring the compliance and financial fraud detection using Benford’s Law. This book: Contains relevant mathematics and examples that demonstrate how to use the concepts presented Features a new chapter on Benford’s Law that explains why we find Benford’s law upheld in so many, but not all, natural situations Presents updated Life insurance tables Contains updates on the Gantt Chart example that further develops the discussion of random events Offers a companion site featuring solutions to the problem sets within the book Written for mathematics and statistics students and professionals, the updated edition of Probably Not: Future Prediction Using Probability and Statistical Inference, Second Edition combines the mathematics of probability with real-world examples. LAWRENCE N. DWORSKY, PhD, is a retired Vice President of the Technical Staff and Director of Motorola’s Components Research Laboratory in Schaumburg, Illinois, USA. He is the author of Introduction to Numerical Electrostatics Using MATLAB from Wiley.

Conventional applications of neural networks usually predict a single value as a function of given inputs. In forecasting, for example, a standard objective is to predict the future value of some entity of interest on the basis of a time series of past measurements or observations. Typical training schemes aim to minimise the sum of squared deviations between predicted and actual values (the 'targets'), by which, ideally, the network learns the conditional mean of the target given the input. If the underlying conditional distribution is Gaus sian or at least unimodal, this may be a satisfactory approach. However, for a multimodal distribution, the conditional mean does not capture the relevant features of the system, and the prediction performance will, in general, be very poor. This calls for a more powerful and sophisticated model, which can learn the whole conditional probability distribution. Chapter 1 demonstrates that even for a deterministic system and 'be nign' Gaussian observational noise, the conditional distribution of a future observation, conditional on a set of past observations, can become strongly skewed and multimodal. In Chapter 2, a general neural network structure for modelling conditional probability densities is derived, and it is shown that a universal approximator for this extended task requires at least two hidden layers. A training scheme is developed from a maximum likelihood approach in Chapter 3, and the performance ofthis method is demonstrated on three stochastic time series in chapters 4 and 5.

A description of the development and application of a stochastic model for predicting the probability distribution of the dissolved-oxygen deficit at points in a stream downstream from a waste source.

This open access book comprehensively covers the fundamentals of clinical data science, focusing on data collection, modelling and clinical applications. Topics covered in the first section on data collection include: data sources, data at scale (big data), data stewardship (FAIR data) and related privacy concerns. Aspects of predictive modelling using techniques such as classification, regression or clustering, and prediction model validation will be covered in the second section. The third section covers aspects of (mobile) clinical decision support systems, operational excellence and value-based healthcare. Fundamentals of Clinical Data Science is an essential resource for healthcare professionals and IT consultants intending to develop and refine their skills in personalized medicine, using solutions based on large datasets from electronic health records or telemonitoring programmes. The book’s promise is “no math, no code”and will explain the topics in a style that is optimized for a healthcare audience.